Proof step e-2dc9098c1ed2fab8

basis_map A007318 → concludes about basis_map_A007318 of Triangle read by rows, s_4(n, k) where s_m(n, k) are the Stirling-Frobenius cycle numbers of order m; n >= 0, k >= 0. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• Triangle read by rows, s_4(n, k) where s_m(n, k) are the Stirling-Frobenius cycle numbers of order m; n >= 0, k >= 0. (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 0006d09d5d8911f755edf64d9ecec99e79c4f068292d668ca8e861afad652af8, 7,412 bytes (1,616 compressed); download JSON

Cited by

• n-61bf3ec06b6c88be (real_rooted)
• n-61bf3ec06b6c88be (one_signed_coefficients)
• n-61bf3ec06b6c88be (hadamard_kernel)